The present invention relates to apparatus and methods for measuring displacements of an object to nanometer accuracy, particularly for use in fabricating modern signal processing components.

In the manufacture of many modern signal processing components it is necessary to fabricate complex patterns to a precision measured on a micron scale. These components include semiconductor integrated circuits, surface acoustic wave (SAW) devices, magnetic and optical memories and many optical components such as DFB lasers, integrated optic devices and spatial light modulators. The ability to produce and measure displacements of the equipment used to fabricate such components to micron accuracy over an area of the order of several square centimetres is therefore essential. There is a trend in these technologies to miniaturise components as much as possible because, for example, not only do you get more transistors per unit area, but smaller transistors operate faster. Similarly, small features extend the frequency range and fidelity of lasers and SAW components. There is therefore a requirement for measuring displacements to a nanometer accuracy over an area of the order of several square centimetres.

In the past such signal processing components were often made using mask making equipment employing large high precision mechanical translation stages followed by photographic reduction. More recently, laser interferometry has been used in which a laser beam reflected from a mirror mounted on a translation stage interferes with a reference laser beam to produce a fringe pattern. This fringe pattern will move one period for a displacement of the translation stage equal to half the wavelength of the laser light. Movement of the fringe pattern to an accuracy of half a fringe is easily measured so for a typical laser wavelength of 500nm an

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accuracy of 125nm is attainable. This accuracy can be improved by interpolation between fringes to an extent- ultimately determined by the signal to noise ratio. Laser interferometry enables the structure on a component or on a mask for a component to be written directly at final size, for example, by using electron-beam lithography.

It is one object of the present invention to provide an apparatus capable of measuring displacements of an object over regions of at least several square centimetres, to nanometer accuracy. It is a further object of the present invention to provide a method capable of measuring displacements of an object over regions of at least several square centimetres, to nanometer accuracy.

According to the first aspect of the present invention there is provided apparatus for measuring displacements of an object including;

a radio frequency (rf) source for generating a primary stable rf electrical signal,

a transducing means for generating an intermediate signal using the primary rf electrical signal at least partly, said intermediate signal having a wavelength less than the wavelength of the primary rf electrical signal,

a phase shifting means interactive in use of the apparatus with the intermediate signal and associated with the object in such a way that a displacement of the object causes the phase shifting means to change the path length of the intermediate signal by an amount directly related to the displacement,

a phase transference means for generating a secondary stable rf electrical

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signal using, at least partly, the intermediate signal after its interaction with the phase shifting means, in such a way that the phase o the interacted intermediate signal is transferred to the secondary rf electrical signal,

and a phase detector for measuring the change of phase of the secondary rf electrical signal relative to the primary rf electrical on displacement of the object.

When a displacement d is applied to an object the path length of the intermediate signal, before it interacts with the phase transference means, is changed by an amount directly related to the displacement. This change in path length d ' , changes the phase of the intermediate signal when it interacts with the phase transference means, by a phase shift p equal to 360 x d ' /l degrees, where 1 is the wavelength of the intermediate signal. The intermediate signal has a wavelength that is less than the wavelength of the rf electrical signal from which it is derived and will generally be an acoustic or optical signal, whose phases are difficult to measure to great accuracy. However, the relative phase between two radio frequency electrical signals can be measured very accurately to a fraction of a degree. The present apparatus transfers the phase shift p from the intermediate signal to an rf electrical signal thus allowing values of p to be measured to an accuracy of a fraction of a degree, by measuring the phase change between the primary and secondary rf electrical signals when the object is displaced. If the phase shift p can be measured to an accuracy of, say one fifth of a degree then the apparatus according to the present invention can measure a displacement d to an accuracy of 1/1800 of 1. Therefore, the smaller 1 is, the more accurately the displacement d can be measured.

For example, if the intermediate signal is an acoustic signal, such as a

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bulk or a surface acoustic wave, with typical wavelengths of between 3000nm and δOOOnm then displacements d of an object can be measured to an accuracy of of between 3000 x 1/1800 nm and δOOO x 1/lδOOnm, ie. between 4.4nm and 1.6nm (assuming d - d ' and that the phase shift p can be measured to an accuracy of one fifth of a degree) . If the intermediate signal is an optical signal with a typical wavelength of several hundred nanometers then displacements of an object can be measured to an accuracy of less than lnm. The present invention enables the structure on a component or on a mask for a component to be written directly at final size and over an area of several square centimetres, for example, by using electron-beam lithography.

Preferably the intermediate signal is an optical signal because this allows displacements to be measured to an accuracy of less than lnm. Also standard techniques from electro-optics technology can be used in the apparatus.

When the intermediate signal is an optical signal the transducing means preferably includes an optical signal source for generating an optical signal, and a mixing means for mixing the optical signal with the primary rf electrical signal to generate a first optical signal that is frequency shifted and a second optical signal that is not frequency shifted, either of which may be the intermediate signal. The optical signal that is chosen to be the intermediate signal is then phase shifted and the other optical signal is used in the phase transference means as a local oscillator for the intermediate signal to generate the secondary rf electrical signal.

In principle the mixing means can take many forms, for example, an rf-driven integrated optic phase- or amplitude- modulator or an integrated optic single-sideband mixer. However, when using these devices it is

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difficult to separate the frequency shifted and unshifted optical signals. More preferably the mixing means is an acousto-optic cell in which bulk radio frequency acoustic waves are induced by an acoustic transducer driven by the primary rf electrical signal and into which the optical signal is directed to generate a deflected first optical signal and an undeflected second optical signal. It is convenient to use an acousto-optic cell as the mixing means because in such a device the first and second signals are automatically separated spatially.

When the intermediate signal is an optical signal the phase shifting means is preferably a mirror onto which the intermediate signal is directed, and the mirror is rigidly secured to the object. If the path length of the intermediate optical signal is changed by a reflection, using a mirror, a displacement d of the mirror results in a change in the path length of the intermediate signal of 2d and so the accuracy of the apparatus can be doubled.

The phase transference means preferably includes a means for mixing the first and second optical signals to produce a difference frequency signal, which is the secondary rf electrical signal and which will carry the phase of the intermediate signal when the mixing takes place. More preferably it includes a photo-diode and a means for directing the first optical signal and the second optical signal onto the photo-diode in such a way that the said signals are overlapping with parallel wavefronts and the same polarisation. Since only one of the optical signals has undergone a frequency shift and only one of the optical signals has undergone a phase shift, the difference frequency signal generated by the photodiode is at the same frequency as the primary rf electrical signal and carries the phase of the intermediate signal.

Alternatively, the intermediate signal can be a rf acoustic wave, such as

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a bulk acoustic wave or a surface acoustic wave. When the intermediate signal is an rf acoustic wave the transducing means includes an acoustic medium and an acoustic transducer driven by the primary rf electrical signal for generating an rf acoustic wave (which is the intermediate signal) in the acoustic medium, and the phase shifting means is interactive, in use of the apparatus, with the acoustic wave and associated with the object in such a way that a displacement of the object changes the path length of the acoustic wave through the acoustic medium between the acoustic transducer and an acoustic wave probe which forms at least part of the phase transference means. The path length of the acoustic wave between the acoustic transducer and the acoustic wave probe can be changed by arranging a displacement of the object to move either the acoustic transducer and medium or the acoustic probe. Preferably, the phase shifting means includes the acoustic transducer and medium which are rigidly secured to the object, and the acoustic probe is fixed so that displacement of the object displaces the acoustic transducer and medium relative to the acoustic probe by an amount directly related to the displacement.

When the intermediate signal is a bulk acoustic wave the acoustic medium is an acousto-optic cell and the acoustic transducer is arranged to induce a rf bulk acoustic wave (the intermediate signal) in the acousto-optic cell and the phase transference means includes an optical signal source which generates an optical signal (which forms the acoustic wave probe) which is directed into the acousto-optic cell and interacts with the bulk acoustic wave to produce a first optical signal that is frequency shifted and a second optical signal that is not frequency shifted, the phase transference means further including a means for mixing the first and second optical signals to produce a difference frequency signal which is the secondary rf electrical signal. The means for mixing the first and second optical signals to produce a difference frequency signal may be a photo diode and a means for directing the first and second optical signals onto the photo-diode in

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such a way that the said signals are overlapping with parallel wavefronts and the same polarisation.

The first optical signal will carry the phase of the bulk acoustic waves at the position where the optical signal from the optical signal source interacts with the bulk acoustic waves in the acousto-optic cell. The phase of the bulk acoustic waves changes continuously with the distance of the waves from the acoustic transducer. Therefore, if the acoustic transducer and the electro-optic cell are rigidly secured relative to the object any displacement of the object will change the position of the interaction between the optical signal and acoustic wave and thus change the phase carried by the first optical signal by an amount directly related to the displacement.

Bulk acoustic waves have typical wavelengths of between 3 to δ microns for typical rf frequencies of around 1GHz and so a phase shift of 1° corresponds to a displacement of between δ and 22nm. Therefore the spatial resolution achievable using bulk acoustic waves in this manner is similar to that achievable using laser interferometry. However this apparatus may have some practical advantages such as reduced size and cost of the components involved, ease of operation and speed of measurement over laser interferometry.

When the phase shift is introduced by bulk acoustic waves the acousto-optic cell preferably comprises a high velocity acoustic material. High velocity crystals tend to have low acoustic attenuation and so allow travels measured in centimetres, which is essential if the area over which the measurements extend is of the order of several square centimetres or more. This is because the acousto-optic cell itself is mounted on the object and so the acoustic wave path must extend over the length of the region over which measurements are to be taken.

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Alternatively the intermediate signal may be a radio frequency surface acoustic wave and the acoustic medium is a surface acoustic wave substrate, the acoustic transducer is arranged to generate a surface acoustic wave in the substrate (which is the intermediate signal) and the phase transference means is a surface acoustic wave probe. The apparatus using surface acoustic waves can achieve a similar accuracy to the apparatus using bulk acoustic waves. However, bulk acoustic waves are preferred as they are less vulnerable to surrounding disturbances, such as air turbulence.

Preferably the rf source for generating the primary rf electrical signal is frequency tuneable so that on displacement of the object the frequency of the primary rf electrical signal can be tuned to restore the relative phase between the primary and secondary rf electrical signals, as measured by the phase detector, prior to the displacement. In this way the precise measurement can be changed from one of phase to one of frequency and it is possible to measure radio frequencies to greater accuracy than radio frequency phases.

According to a second aspect of the present invention there is provided a method for measuring very small displacements of an object which includes;

generating a primary stable radio frequency (rf) electrical signal,

generating an intermediate signal using the primary signal at least partly, said intermediate signal having a wavelength less than the wavelength of the primary rf electrical signal,

interacting the intermediate signal with a phase shifting means associated with the object, in such a way that a displacement of the object causes

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-> the phase shifting means to change the path length of the intermediate signal by an amount directly related to the displacement,

applying a displacement to the object,

generating a secondary stable rf electrical signal using, at least partly, the intermediate signal after its interaction with the phase shifting means, in such a way that the phase of the intermediate signal is transferred to the secondary rf signal,

and measuring the change of phase of the secondary rf electrical signal on displacement of the object, relative to the primary rf electrical signal.

Preferably the intermediate signal is an optical signal. When the intermediate signal is an optical signal generating the intermediate signal preferably includes generating an optical signal and mixing the optical signal with the primary rf electrical signal to generate a first optical signal that is frequency shifted and a second optical signal that is not frequency shifted, either of which may be the intermediate signal. More preferably the mixing of the optical signal with the primary rf electrical signal includes inducing bulk radio frequency acoustic waves in an acousto-optic cell using an acoustic transducer driven by the primary rf electrical signal and directing the optical signal into the acousto-optic cell to produce a deflected first optical signal and an undeflected second optical signal.

Preferably generating the secondary rf electrical signal includes mixing the first and second optical signals to produce a difference frequency signal which is the secondary rf electrical signal. More preferably it includes directing the first and second optical signals onto a photo-diode in such a way that the said signals are overlapping with parallel

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wavefronts and the same polarisation.

Alternatively the intermediate signal may be a radio frequency acoustic wave such as a bulk acoustic wave or a surface acoustic wave. When the intermediate signal is an acoustic wave then generating the intermediate signal includes generating an acoustic signal (which is the intermediate signal) in an acoustic medium using an acoustic transducer driven by the primary rf electrical signal, and generating the secondary rf electrical signal includes interacting the acoustic signal with an acoustic probe which forms at least part of the phase transference means. Preferably displacement of the object displaces the acoustic transducer and medium relative to the acoustic probe by an amount directly related to the displacement, thus changing the path length of the acoustic wave between the acoustic transducer and the acoustic probe by the same distance.

Measuring the change of phase of the secondary rf electrical signal may include frequency tuning the primary rf electrical signal on displacement of the object to restore the relative phase between the primary and secondary rf electrical signals prior to the displacement.

The method according to the second aspect of the present invention has the same advantages as discussed above with reference to the apparatus of the first aspect.

Apparatus and methods according to the present invention will now be described by way of example only with reference to the following Figures in which:

Figure 1 shows a first embodiment of apparatus according to the present invention in which the intermediate signal is a surface acoustic wave.

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Figure 2 shows a second embodiment of the apparatus according to the present invention in which the intermediate signal is a bulk acoustic wave and which incorporates an acousto-optic Bragg cell mounted on a travelling stage.

Figure 3a shows a third embodiment of the apparatus according to the present invention in which the intermediate signal is an optical signal and which incorporates a fixed acousto-optic Bragg cell and a mirror mounted on a travelling stage.

Figure 3b shows an alternative modified version of the apparatus in Figure 3a.

Referring first to Figure 1 in which the intermediate signal is a surface acoustic wave (SAW). A piezoelectric SAW substrate 4, for example quartz or LiNb0 ₃ , is mounted on a precision travelling stage 2, operated by a stepper motor system, which can be moved in small incremental steps in the directions shown by the arrow 18. Surface acoustic waves are induced in the SAW substrate 4 by the SAW interdigital transducer 6 to which primary radio frequency waves are supplied from a stable radio frequency source δ via a flexible cable 10. A SAW absorber 12 is located at the opposite end of the SAW substrate 4 from the transducer 6 to absorb the surface acoustic waves so that they are not reflected back across the substrate 4. There is also a SAW absorber (not shown) at the end of the SAW substrate 4 adjacent to the transducer 6. A fixed SAW probe 14 taps off a portion of the surface acoustic wave and converts it into a secondary electrical rf signal. This secondary rf electrical signal and primary signal from the rf source δ are fed to a phase detector 16, for example a vector voltmeter set up to the measure relative phase of the two rf electrical signals.

In operation the travelling stage 2 is positioned at a zero displacement

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setting and the relative phase between the primary rf electrical signal from the source 8 and the secondary rf electrical signal from the probe 14 is noted. When the stepper motor 2 is moved the piezoelectric SAW substrate 4 moves relative to the fixed probe 14 thus changing the path length of the surface acoustic waves from the transducer 6 to the probe 14. This change in path length changes the phase of the surface acoustic wave that is tapped off by the probe 14 and thus the phase of the secondary rf electrical signal that is fed to the phase detector 16. Therefore the relative phase of the primary rf electrical signal from the source δ and the secondary rf electrical signal from the probe 14 changes by an amount directly related to the movement of the translation stage 2.

An rf electrical signal generally has a frequency of around 1GHz which will induce surface acoustic waves in a typical SAW substrate 4 with wavelengths of between 3 and δ microns. Therefore a change in the relative phase measured by the detector 16 of 1° corresponds to a displacement of the translation stage 2 of 1/360 times the wavelength of the surface acoustic wave tapped off by the probe 14. For example, if the surface acoustic wave induced on the SAW substrate has a wavelength of 3000nm then a change in the relative phase of 1°, as measured by the phase detector corresponds to a displacement of about δnm. State of the art phase detectors can measure relative phase to an accuracy of at least 0.2° giving the apparatus in Figure 1 a spatial resolution of between about 1 and 4nm depending on the wavelength of the surface acoustic wave.

The embodiment of the present invention shown in Figure 2 uses bulk acoustic waves as the intermediate signal as opposed to surface acoustic waves. The apparatus in Figure 2 includes a laser 26, which should be a stable source, ie. have a large coherence length and a constant intensity, of suitable power to provide a good signal to noise ratio. A Helium Neon laser with a coherence length of around 100 metres may be used. The laser

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beam from the laser 26 is focussed (although focussing is not always necessary) by the convex lens 2δ into an acousto-optic Bragg cell 20. The acoustic medium of the Bragg cell 20 should have a low acoustic loss (which implies the use of a single crystal) , be stable, available in large sizes (several cms) at acceptable cost, optically transparent and preferably have a small or zero effective temperature coefficient of acoustic velocity in its mounted state. The acoustic medium of the Bragg cell 20 may be, for example, quartz, sapphire, GaP, LiNb0 ₃ , MgAl^ or A1 ₂ 0 ₃ . The Bragg cell 20 is mounted rigidly, for example is bolted directly, on a translation stage 22 which can be stepped electrically in sub-micron increments. An acoustic transducer 24 is located at one end of the Bragg cell 20 and a primary rf electrical signal is fed to the transducer 24 from a network analyser 32 via a power amplifier 30. The network analyser 32 could be replaced by the stable radio frequency source 6 and phase detector 16 of Figure 1. The acoustic transducer 24 induces rf bulk acoustic waves in the Bragg cell 20.

If a measurement has to be made over a length several centimetres, ie. the required travel is several centimetres, the Bragg cell 20 must have a length of several centimetres and the acoustic wave produced by the transducer 24 is required to travel as a collimated beam for several centimetres. Therefore the diameter, D of the transducer 24 should be such that

D ² / ' lacoust .i.c > req^uired travel

where Iacous _t_.i .c is the waveleng°th of the acoustic waves. Since will be of the order of 5 microns, D should be of the order of 1mm and the acoustic Bragg cell 20 should have a cross section of around 1cm ² to avoid acoustic reflections from its sidewalls. The above has assumed an acoustically isotropic medium. The transducer diameter of 1mm is greater

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than might normally be employed, resulting in a low electrical impedance. However, the required electrical bandwidth of the transducer 24 is modest when compared to most other applications so that the transducer 24 can be matched electrically to say a 50ohm source with little difficulty. A bonded LiNbO, transducer, for example, may be used.

When the laser beam is directed into the Bragg cell 20 two beams 3 , 3 emerge from the cell. The drive power for the acoustic transducer 24 should ideally be such that approaching 50% of the laser beam is deflected leaving 50% undeflected as this optimises the signal from photo-diode 44. The deflected beam 36 of frequency W _o + W, where W _o is the frequency of the laser beam and W is the frequency of the primary rf signal from the network analyser 32, is directed via lens 3δ onto beamsplitter 40. The undeflected beam 3 of frequency W _o is directed via lens 3δ and mirror 39 onto beamsplitter 40, which may be a cube beamsplitter. The arrangement of the lens 3δ, mirror 39 and beamsplitter 4θ ensures that the deflected and undeflected beams 3 and 34 respectively are overlapping, have parallel wavefronts and the same polarisation when they are focussed onto a 2GHz bandwidth photo-diode 44 via a lens 42. The photo-diode 44 preferably has as large an area as possible to enable interception of the combined laser beams 34 and 3 which may be up to 1mm in diameter if not focussed down by a lens such as the lens 42. The secondary rf electrical signal from the photo-diode 44 is then fed via a 3dB pad 46 (which forms a d.c. return for the photo-diode 44) and a preamplifier 4δ to the network analyser 32. The network analyser 3 measures the relative phase between the primary rf electrical signal from the network analyser 3 and the secondary rf electrical signal from the preamplifier 4δ.

In operation the translation stage 22 is positioned at a zero displacement setting and the relative phase between the primary rf electrical signal from the network analyser 32 and the secondary rf electrical signal from

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the preamplifier 48 is noted. When the stepper motor 22 is moved the acousto-optic Bragg cell 20 moves relative to the laser beam directed from the laser 26 via the lens 28 into the cell 20. The detailed acousto-optic interaction between the laser beam and the rf bulk acoustic waves is a complicated mixture of diffraction and reflection which is not discussed here in detail, but the laser beam effectively replaces the fixed mechanical probe 14 of Figure 1. The deflected optical beam 36, incorporates the phase of the rf bulk acoustic wave from which it is scattered in the cell 20. Therefore when the stepper motor 22 is displaced the path length through which the bulk acoustic waves travel from the transducer 24 before interacting with the laser beam is changed. Thus the phase of the bulk acoustic waves which interacts with the laser beam shifts which shifts the phase of the deflected optical signal 3 . The secondary rf electrical signal from the photo-diode 44 incorporates this phase shift and so the relative phase between the primary rf electrical signal from the network analyser 32 and the secondary rf electrical signal from the preamplifier 48 changes. Therefore the relative phase measured by the network analyser 32 changes by an amount directly related to the movement of the stepper motor 22.

An rf signal generally has a frequency of around 1GHz which will induce bulk acoustic waves in a typical acousto-optic Bragg cell 20 with wavelengths of between 3 and 8 microns. Therefore a change in the relative phase measured by the network analyser of 1° corresponds to a displacement of the translation stage 22 of 1/360 times the wavelength of the acoustic wave that interacts with the laser beam. For example, if the bulk acoustic wave induced in the Bragg cell 20 has a wavelength of 3000nm, then a change in the relative phase of 1° as measured by the network analyser 32 corresponds to a displacement of δnm. State of the art phase detectors can measure relative phase to an accuracy of at least 0.2° giving the apparatus in Figure 2 a spatial resolution of between

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about 1 and 4nm depending on the wavelength of the bulk acoustic waves.

The arrangement in Figure 2 can be made more stable by eliminating lenses 38 and 42 and bringing the mirror 39 beamsplitter 40 and photo-diode 44 as close as possible to the Bragg cell 20. This reduces the effect of vibrations in components, reduces the effect of air turbulence in the critical region where the beams 3 and 36 are split spatially and reduces innacuracies caused when the coherence length of the laser is of the same order as the differential pathlength. The air turbulence effects where the beams 34 and 36 are split can be eliminated be employing a glass block in this region.

In the apparatus in Figure 3 the intermediate signal is an optical signal. The arrangement shown in Figure 3a is similar to the one shown in Figure 2, except that the acoustic Bragg cell 20 is fixed in place and the displacement to be measured alters the path length of the deflected optical wave 36. The apparatus in Figure 3a includes a laser 26, the laser beam from which is directed into a Bragg cell 20, which is fixed in place. The requirements from the Bragg cell 20 are less than those in the Figure 2 arrangement because a large acoustic path is no longer necessary. Acoustically slow media, such as Te0 ₂ may be preferable since it can provide a large angular separation of the beams 34 and 36 at a modest rf frequency. An acoustic transducer 24 is located at one end of the Bragg cell 20 and a primary rf electrical signal is fed to the transducer 24 from a stable rf source 50. Similarly to the arrangement in Figure 2, the acoustic transducer 24 induces rf bulk acoustic waves in the Bragg cell 20. Thus when the laser beam is directed into the Bragg cell 20 the two laser beams 3 and 36 emerge from the cell.

The undeflected beam 34 is directed onto beamsplitter 58. The deflected beam 36 is directed onto a mirror 6 via a beamslitter 52. The beam

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reflected from the mirror 6 is directed via beamsplitter onto beamsplitter 8. The mirror 56 is mounted on the travelling stage 22 (not shown) so that the mirror 6 moves in the direction of the arrow. Movement of the mirror 56 therefore alters the path length of the beam 36. The arrangement of the beamsplitter 58 ensures that the deflected and undeflected beams 36 and 34 respectively are overlapping and have parallel wavefronts and the same polarisation when they are incident on the photo-diode 60. The secondary rf electrical signal from the photo-diode 6θ is then fed to a vector voltmeter 62 which measures the relative phase between the secondary signal from the photo-diode 60 and the primary signal from the rf source 50. To improve efficiency, beamsplitter 52 could be made a polarising beamsplitter, and used in conjunction with optical quarter and half wave plates in such a manner as to ensure that the optical beams arrive at the detector with the same polarisation.

When the mirror is displaced by a distance d the path length of the deflected signal 36 is changed by 2d, which produces a phase change, in degrees, in the deflected signal 36 of

360(2d/Z _optical )

where l _{o tical} is the wavelength of the deflected signal 36. Therefore if the vector voltmeter measures a relative phase change of 1°, for an optical wavelength of typically 500nm the displacement of the travelling stage in Figure 3 is

( ^x Iopt.i.cal./'2)'/'3-'60 lnm.

The function of the Bragg cell 20 is to produce the frequency shifting operation and other techniques such as rf-driven integrated optic phase or amplitude modulators or single sideband mixers could alternatively be

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used. The Bragg cell 20 does have the advantage of being inherently a single-sideband mixer and naturally provides the spatial separation of the frequency shifted and unshifted beams necessary for interferometry.

Figure 3b shows a modified version of Figure 3a and uses the like indicator numerals for like parts of the apparatus. The apparatus in Figure 3b works in the same way as the apparatus in Figure 3 except that the undeflected optical beam 34 is phase shifted instead of the deflected optical beam 36.

An alternative to using the detector 16 in Figure 1, the network analyser 32 in Figure 2 or the vector voltmeters 62 in Figures 3 and 3b would be to use a simple double balanced mixer, which for constant levels of the secondary rf electrical signal and primary rf electrical signal will generally have a sinusoidal output with phase, the said output being zero at phase quadrature. A coarse measurement could then be made of the displacement of the translation stage by counting cycles (ie. changes in phase of 360°) and then a fine measurement can be made by adjusting the frequency of the rf signal fed to the transducer to restore the zero-output (phase quadrature) condition. The change in frequency required to restore phase quadrature can be measured to great accuracy. This alternative has the advantage of only being operated at one point, the zero output point, which is insensitive to amplitude variations of the primary and secondary rf electrical signals. Another possibility might be to mix the primary and secondary rf electrical signals down with a common local oscillator to enable the phase measurement to be made at a convenient lower frequency.

There are two kinds of acousto-optic interactions, isotropic interactions and anisotropic interactions. The above description has assumed an isotropic acousto-optic interaction. Alternatively, an anisotropic

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acousto-optic interaction in which the deflected optical signal is phase shifted by 90° can be used in the apparatus described above provided that the 90° phase shift is compensated so that that the deflected and undeflected optical signal are overlapping and have parallel wavefronts and the same polarisation when they are incident on the photo-diode.

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